Simplify the following expression: $ y = \dfrac{-2t - 3}{9t + 6} - \dfrac{1}{5} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-2t - 3}{9t + 6} \times \dfrac{5}{5} = \dfrac{-10t - 15}{45t + 30} $ Multiply the second expression by $\dfrac{9t + 6}{9t + 6}$ $ \dfrac{1}{5} \times \dfrac{9t + 6}{9t + 6} = \dfrac{9t + 6}{45t + 30} $ Therefore $ y = \dfrac{-10t - 15}{45t + 30} - \dfrac{9t + 6}{45t + 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-10t - 15 - (9t + 6) }{45t + 30} $ Distribute the negative sign: $y = \dfrac{-10t - 15 - 9t - 6}{45t + 30}$ $y = \dfrac{-19t - 21}{45t + 30}$